I cut the panels from two ply cardboard sheets using an Olfa knife. It is very important to use a really sharp edge - and I always start a new ball with a new blade and change it frequently -
as soon as the cardboard edges fray.

ALWAYS cut away from your hand NEVER towards it.

I use red Tuck Tape to join the panels. Made for permanantly joining plastic vapour barrier, this is the ONLY tape strong enough to hold the balls together.

I use WELDBOND white glue - and often add a little water to make it more easily brushable.

I cover
the outside of the joins between the panels with 2 inch brown paper strips - I brush WELDBOND on to the strips and then press them in place. The strips are cut from yard waste bags. These bags use a double layer of strong paper, so one bag gives
lots of strips. The strips do not usually lie flat when first laid down - they cockle and crinkle. If you use a hot iron about 20 minutes after the strips have been placed - you can elininate most of these irregularities to get
a completely flat surface.

I use latex paint with primer incorporated. It usually takes two coats for sufficient coverage.

Paper strips in place over joins - during this phase I used drywall tape - I have since replaced this material with brown kraft paper - drywall tape is very white and rather thick and stiff- It is difficult to get it to lie flat and needs 3 coats of paint for coverage.

The easiest source of kraft paper is from garden waste bags - such as this one from Home Depot. This gives you two 4' x 4' sheets of brown paper.

For making the snowballs - the balls are first painted white and then covered with quilt batting. I use hot melt glue to position the batting and pressing the seams together.
I've also tried fabric glue - but is is very expensive and does not work as well as hot melt glue.